Can a single vertex be rotated?
From the Blender wiki.


If the vertex pertains to one or more faces, its normal is the
interpolated value of all the normals of these faces.
If the vertex does not pertain to any face, its normal is aligned
with the line from the object’s Origin passing through this vertex.


On a unconnected vertex the normal will always point away from the object's origin. On a vertex connected with one or more faces (like stacker said) Vertex normals are interpolated from face normals.